def wide_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/mulw.bend:117

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/poly.bend as PL
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fold.bend as FD

117def wide_mod(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +zs: List<&2, U32>, +hl: {LM.lea(zs, WD.sc(21n, one)) == True{} : Bool}, +hge: {PL.len_ge(32n, zs) == True{} : Bool}) -> {Nat.mod(FS.value(F.wide(zs)), 1n+pp) == Nat.mod(FS.value(zs), 1n+pp) : Nat}:
118  +k21 = WD.sc(21n, one)
119  +T = F.take(32n, zs)
120  +D = F.drop(32n, zs)
121  +okT = PL.take_okb(32n, zs, k21, hge, hl)
122  +leD = PL.drop_lea(32n, zs, k21, hl)
123  +leS = PL.scal_lea(one, h1, 38, D, 38n, k21, N.le_refl(38n), leD, m38_lt(one, h1))
124  +VT = FS.value(T)
125  +VD = FS.value(D)
126  +ew = PL.addl_val(one, h1, T, F.scal(38, D), k21, Nat.mul(38n, k21), LM.okb_lea(32n, T, k21, okT), leS, wsum_lt(one, h1))
127  +es = PL.scal_val(one, h1, 38, D, 38n, k21, N.le_refl(38n), leD, m38_lt(one, h1))
128  +ew2 = Equal.trans(Nat, FS.value(F.wide(zs)), Nat.add(VT, FS.value(F.scal(38, D))), Nat.add(VT, Nat.mul(38n, VD)), ew, M.cong_r(VT, FS.value(F.scal(38, D)), Nat.mul(38n, VD), es))
129  +ez = Equal.trans(Nat, FS.value(zs), Nat.add(VT, LM.sh(T, VD)), Nat.add(VT, LM.shn(32n, VD)), PL.take_drop_val(32n, zs), M.cong_r(VT, LM.sh(T, VD), LM.shn(32n, VD), LM.sh_okb(32n, T, k21, VD, okT)))
130  +ef = FD.fold_id(one, h1, pp, hP, VT, VD)
131  +q = Nat.add(VD, VD)
132  +ez2 = Equal.trans(Nat, FS.value(zs), Nat.add(VT, LM.shn(32n, VD)), Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), ez, Equal.trans(Nat, Nat.add(VT, LM.shn(32n, VD)), Nat.add(Nat.mul(q, 1n+pp), Nat.add(VT, Nat.mul(38n, VD))), Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), ef, M.cong_r(Nat.mul(q, 1n+pp), Nat.add(VT, Nat.mul(38n, VD)), FS.value(F.wide(zs)), Equal.sym(Nat, FS.value(F.wide(zs)), Nat.add(VT, Nat.mul(38n, VD)), ew2))))
133  Equal.trans(Nat, Nat.mod(FS.value(F.wide(zs)), 1n+pp), Nat.mod(Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), 1n+pp), Nat.mod(FS.value(zs), 1n+pp), Equal.sym(Nat, Nat.mod(Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), 1n+pp), Nat.mod(FS.value(F.wide(zs)), 1n+pp), NR.absorb(pp, q, FS.value(F.wide(zs)))), M.cong_mod(1n+pp, Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), FS.value(zs), Equal.sym(Nat, FS.value(zs), Nat.add(Nat.mul(q, 1n+pp), FS.value(F.wide(zs))), ez2)))